# Occurrence and seasonal variability of Dense Shelf Water Cascades along Australian continental shelves

## Abstract

Transport of water between the coast and the deeper ocean, across the continental shelf, is an important process for the distribution of biota, nutrients, suspended and dissolved material on the shelf. Presence of denser water on the inner continental shelf results in a cross-shelf density gradient that drives a gravitational circulation with offshore transport of denser water along the sea bed that is defined as Dense Shelf Water Cascade (DSWC). Analysis of field data, collected from multiple ocean glider data missions around Australia, confirmed that under a range of wind and tidal conditions, DSWC was a regular occurrence during autumn and winter months over a coastline spanning > 10,000 km. It is shown that even in the presence of relatively high wind- and tidal-induced vertical mixing, DSWCs were present due to the strength of the cross-shelf density gradient. The occurrence of DSWC around Australia is unique with continental scale forcing through air-sea fluxes that overcome local wind and tidal forcing. It is shown that DSWC acts as a conduit to transport suspended material across the continental shelf and is a critical process that influences water quality on the inner continental shelf.

## Introduction

Globally, the coastal ocean is the receiving basin for input of suspended and dissolved matter that includes nutrients, biota and pollutants and represents an important component of the ocean environment, connecting the terrestrial system to the deeper ocean1. Transport processes that contribute to the exchange of water between the coast and deeper regions: cross-shelf exchange, has been defined as one of the central problems in coastal physical oceanography2. Majority of inputs to the coastal zone are through fresh water sources such as rivers and anthropogenic discharges. As these inputs are usually buoyant, they are transported along the ocean surface layer subject to the prevailing hydrodynamic regime and are easily identified in the field and in satellite imagery. If the spatial scale is unrestricted by coastal features and under relatively low mixing conditions, river plumes can influence the hydrodynamics to hundreds of kilometres from the source region3,4. These systems have been subject to many investigations over the past decades being defined as river plumes or Regions of Freshwater Influence (ROFI) where the hydrodynamic regime is governed by the positive density gradient between lower salinity riverine water and higher salinity oceanic water3. In ROFI, buoyancy input from freshwater sources exceeds that from changes in heat and freshwater fluxes across the ocean surface.

Regions that experience a Mediterranean climate (dry hot summers, mild cooler winters and low precipitation) are subject to high rates of evaporation and negligible river input resulting in a net loss of fresh water from the coastal region. Therefore, coastal water bodies become more saline than the surrounding ocean water with density decreasing from the coast to the ocean (i.e. a negative density gradient). With the advent of cooling during late autumn and winter, this density contrast is increased. Here, buoyancy input from heat and freshwater fluxes across the ocean exceed that due to freshwater sources and thus are opposite to that in ROFI regions where the density is increasing from the coast to the ocean. Rather than having a buoyant plume due to freshwater input, the negative density gradient drives an offshore-directed flow of denser water along the seabed (Fig. 1)5,6,7,8. A similar feature to that observed in ‘inverse’ estuarine systems located in Mediterranean climates with negligible or intermittent freshwater input and loss of freshwater through evaporation9,10. In coastal regions, the buoyancy-driven gravity current is defined as Dense Shelf Water Cascade (DSWC)5,8,11,12,13,14 and has mainly been considered as a high‐latitude process11,13. DSWCs documented around the Mediterranean Sea are episodic and their formation related to specific atmospheric conditions. For example, in the northern Adriatic Sea, DSWC occurs only in years where there is substantial cooling of the whole water column associated with wintertime bora winds, preconditioned by a lower-than-usual river discharges15.

Evidence for DSWC has been provided in locations around Australia based on single field experiments lasting over a period of about 1 month6,7,8,9,13,14,16,17,18. Majority of these studies examined the export of higher salinity water from large inverse estuary systems6,7,16,18 with only two studies examining shelf regions13,17. Seasonal variation in DSWC was identified as a major feature through the deployment of ocean gliders along the Rottnest continental shelf5. This paper is an extension of the work by Pattiaratchi et al.5 from a single location and season to multiple locations and seasons to examine the generating mechanisms and seasonal variability of DSWC formation around Australia spanning a coastline > 10,000 km and a range of wind and tidal conditions.

The oceans surrounding Australia experience some of the highest evaporation (>2.5 m per annum19) and negative heat flux (cooling) rates globally. Climatological means of the freshwater budget (evaporation-precipitation) and the net heat flux indicate that from January to June the mean evaporation rates are ~ 6 mmday−1 (Figure S1) with the spatial extent of the high evaporation regions during May-June (late autumn). In contrast, the net heat flux is positive (~ 750 Wm−2) in January-February and changes to a negative heat flux (<−1000 Wm−2) in May-June. High rates of cooling are highlighted by the sea surface temperature climatology in Australian shelf waters20 during May and June that indicate a band of colder water closer to the coast (Fig. 2). Due to high evaporation rates (Figure S1), these coastal waters also contain elevated salinities. Combination of higher salinity and colder water at the coast lead to higher density water on the inner continental shelf creating horizontal density gradients that drive DSWC. In this paper, occurrence of DSWC around Australia and their seasonal variability, both spatially and temporally, are examined using an extensive ocean glider data set obtained between 2008 and 201921 that included 254 cross-shelf transects selected from over 126 glider missions from eight different regions. The main aims of this paper are to (1) identify and document the occurrence of DSWC around Australia; and, (2) define the main controlling mechanisms and their seasonal variability. The extensive data set, collected using ocean gliders, included large spatial scales (>10,000 km) and enabled the identification of seasonal (monthly) variability. DSWC were observed at different locations independent of the wind and tidal regime due to the strength of the negative cross-shelf density gradient (denser water along the coast).

### Theory

Circulation and mixing on continental shelves are largely driven by wind, tides and input of buoyancy at the boundaries (terrestrial and the air-sea interface). In the shallow continental shelves considered here, with mean water depths less than the Ekman depth (at Two Rocks, the Ekman depth is 70 m whilst mean water depth is 40 m) the influence of earth rotation is minimal1. Circulation patterns resulting from interactions between these mechanisms together with complex topography of continental shelves are challenging to measure and to unravel. Numerical simulations that include idealised setups have been used to isolate the role of different processes and to develop predictive capability22,23. However, simple theories for important aspects of buoyancy-influenced coastal currents have been developed and evaluated with field campaigns and numerical models that have contributed to a broad understanding of coastal dynamics.

Vertical stratification in the coastal ocean is controlled by buoyancy fluxes that promotes stratification whilst turbulent kinetic energy generated through wind and tides promotes mixing24,25. The competition between buoyancy and mixing inputs determine stratification status of the water column. Buoyancy fluxes include horizontal advection of water, due to a longitudinal density gradient $$(\frac{\partial \rho }{\partial x})$$, from a region of higher buoyancy over denser water (e.g. river plumes) or lower buoyancy along the bottom (e.g. DSWC) by a vertically sheared flow. This mechanism was termed “straining” by Simpson et al.24. Ratio of the longitudinal density gradient (stratifying force) to vertical mixing (destratifying force) is defined as the horizontal Richardson number (Rix), also defined as the Simpson number24,26,27:

$$R{i}_{x}\approx \frac{g}{\rho }\frac{{h}^{2}}{{u}_{\ast }^{2}}\frac{\partial \rho }{\partial x}$$
(1)

where, h = mean water depth; ρ = mean seawater density; and, u* = friction velocity; Monismith et al.26 proposed that values of Rix > O(1) reflected a dominance of stratification by horizontal density gradients over tidal mixing, resulting in a stratified water column. Burchard28 modified Eq. (1) to include wind mixing:

$$R{i}_{x}\approx \frac{g}{\rho }\frac{{h}^{2}}{{u}_{\ast wt}^{2}}\frac{\partial \rho }{\partial x}$$
(2)

with $${u}_{\ast wt}^{2}={u}_{\ast t}^{2}+{u}_{\ast w}^{2}$$ and $${u}_{\ast t}^{2}={k}_{D}{u}_{b}^{2}$$ and $${u}_{\ast w}^{2}={k}_{s}\frac{{\rho }_{a}}{\rho }{W}^{2}$$. Here, kD and ks are the bottom and surface drag coefficients, respectively and ρa is the density of air and U is the near bed velocity (tidal) and W is the wind speed.

Numerical simulations by Horwitz29 indicated that cross-shelf transport was controlled by the horizontal Richardson number (Rix) and found that for increasing density in the direction of the wind stress (for this study onshore winds), the horizontal density gradient increased the cross-shelf transport by strengthening the stratification and reducing mixing. For wind stress opposing the density gradient, the cross-shelf density gradient decreased the cross-shelf transport by enhancing vertical mixing.

DSWCs are generated through the formation of a cross-shelf density gradient by surface cooling and/or evaporation5. Consider an initially homogeneous water body on a continental shelf with a sloping bathymetry subject to uniform surface cooling (or heating). Here, the shallower water cools (heats) more rapidly compared to those in deeper water (‘differential heating/cooling’) that results in the formation of a cross-shelf density gradient30. The density gradient provides the buoyancy input that drives the DSWC. In contrast, turbulent kinetic energy resulting from wind and/or tidal action promotes vertical mixing. When the buoyancy input dominates over turbulent wind and/or tidal mixing, a DSWC is formed (Fig. 1a). In the case of vertical mixing being stronger than the buoyancy input, a vertically mixed water column is present although the cross-shelf density gradient still exists (Fig. 1b).

In the relatively narrow shallow continental shelf regions considered in this study, the dynamical balance consists of buoyancy, Coriolis, wind and tidal induced vertical mixing and friction. This results in the DSWC being moved offshore and deflected to the left at some angle to the coastline23. Majority of the locations contained relatively uniform bathymetry with a slight offshore gradient. There were no major topographic features (e.g. reefs, islands etc) in regions where glider deployments were made mainly due to the requirement for safe operation of the gliders.

The potential energy anomaly (ϕ) method proposed by Simpson et al.24 was used here to investigate physical processes governing the DSWC. ϕ values express the vertical stability of the water column and is the amount of energy per unit volume (J m−3) required to vertically mix a stratified water column:

$$\phi =\frac{g}{h}{\int }_{-h}^{0}(\bar{\rho }-\rho )zdz$$
(3)

with:

$$\bar{\rho }=\frac{1}{h}{\int }_{-h}^{0}\rho (z)dz$$
(4)

where, g is the gravitational acceleration (ms−2), z is the vertical coordinate pointing upward from the seabed, $$\bar{\rho }$$ is the depth-averaged density (kgm−3) and ρ(z) is the seawater density (kgm−3) at depth z, and h is the total water depth (m).

Whilst ϕ explains the instant state of water column stability, the temporal change in ϕ reflects different processes that are related to advection, vertical mixing through wind and tidal stirring and stratifying mechanisms through buoyancy input24.

Burchard and Hofmeister31 derived a time-dependent equation for ϕ based on the advection of potential temperature and salinity equations, the continuity equation and an equation of state for the potential density. The derived equations, that are more suitable for the analysis of three-dimensional numerical model output represented changes in ϕ through advection by currents, vertical mixing, buoyancy fluxes, sinks and sources of potential density and horizontal eddy diffusive density fluxes (for further explanation of these terms and the detailed derivation see Burchard and Hofmeister31, de Boer et al.32 and Kokkos and Sylaios33).

We follow the approach of Simpson et al.24 and describe the temporal change of ϕ due to mechanical mixing (wind and tidal stirring) and stratifying mechanisms (e.g. air-sea heat flux and buoyancy flux):

$${\left[\frac{\partial \phi }{\partial {\rm{t}}}\right]}_{total}={\left[\frac{4{{\rm{\varepsilon }}{\rm{k}}}_{{\rm{D}}}{\rm{\rho }}}{3{\rm{\pi }}}\frac{|{{{\rm{u}}}_{{\rm{b}}}}^{3}|}{{\rm{h}}}\right]}_{tidal}+{\left[{{\rm{\delta }}{\rm{k}}}_{{\rm{S}}}{{\rm{\rho }}}_{{\rm{a}}}\frac{|{{\rm{W}}}^{3}|}{{\rm{h}}}\right]}_{wind}+{\left[\frac{1}{320}\frac{{{\rm{g}}}^{2}{{\rm{h}}}^{4}}{{{\rm{\rho }}{\rm{N}}}_{{\rm{z}}}}{\frac{\partial {\rm{\rho }}}{\partial {\rm{x}}}}^{2}\right]}_{gravitational}$$
(5)

where, the first and second terms on the right represents the mechanical mixing due to the action of tides and wind, respectively. The third term is the advection of buoyancy flux represented by a horizontal density gradient defined as the gravitational circulation24. Values for different coefficients are given by Simpson et al.24 and Nahas et al.16. δ and ε represent the efficiency of conversion of wind and the tidally-generated turbulent kinetic energy into potential energy (δ = 0.039; ε = 0.0038); kD and ks are the surface and bottom drag coefficients (kD = 2.5 × 10−3; ks = 6.4 × 10−5); ρa is the density of air (1.2 kgm−3); ub and W represent bottom current and wind speeds (ms−1), respectively. The third term defines the buoyancy flux through the advection of higher density water due to the cross-shelf density gradient. NZ is the vertical eddy viscosity coefficient assumed to be 1~ 17 × 10–5 m2s−1 (see also Mahjabin et al. 30).

When the change in potential energy anomaly (ϕ) over time is positive (/dt > 0), the water column is stable and stratified, and when /dt < 0 the water column is vertically mixed and when ϕ = 0, it is vertically homogeneous with the input of buoyancy exactly balanced by vertical mixing. For the water column to be vertically stratified the necessary condition is:

$${\left[\frac{1}{320}\frac{{{\rm{g}}}^{2}{{\rm{h}}}^{4}}{{{\rm{\rho }}{\rm{N}}}_{{\rm{z}}}}{\frac{\partial {\rm{\rho }}}{\partial {\rm{x}}}}^{2}\right]}_{gravitational} > {\left[\frac{4{{\rm{\varepsilon }}{\rm{k}}}_{{\rm{D}}}{\rm{\rho }}}{3{\rm{\pi }}}\frac{{{{\rm{u}}}_{{\rm{b}}}}^{3}}{{\rm{h}}}\right]}_{tidal}+{\left[{{\rm{\delta }}{\rm{k}}}_{{\rm{S}}}{{\rm{\rho }}}_{{\rm{a}}}\frac{{{\rm{W}}}^{3}}{{\rm{h}}}\right]}_{wind}$$
(6)

Equation (6) implies that when the horizontal density gradient $$(\frac{\partial \rho }{\partial x})$$is able to overcome vertical mixing through tidal and wind action, DWSC should occur. In contrast if the action of tidal- and/or wind- induced vertical mixing was higher (i.e., higher values of U and/or W) the water column will be vertically mixed thus inhibiting the formation of DSWC.

## Results

Ocean glider data collected between 2008 and 2019 from 8 different locations around the Australian continent spanning a coastline > 10,000 km (Fig. 3) were analysed and included 254 transects selected from 126 separate ocean glider deployments. The results are presented to highlight the DSWC events as measured from the Slocum ocean glider observations along cross-shelf transects and include: typical examples of DSWC from Two Rocks and the Pilbara; occurrence of DSWC around Australia, seasonality of DSWC; and, examination of the driving mechanisms. Although all the data were used to calculate the cross-shelf density gradients, only selected profiles are presented here.

Typical cross-shelf transects for Two Rocks (May 2016) and Pilbara (July 2012) indicated that both temperature and salinity contributed to the dense water formation (Fig. 4). At Two Rocks, the difference between inshore and offshore waters for temperature and salinity was 2 °C and 0.2 units, respectively whilst in the Pilbara the difference was 2.5 °C and 0.6 units. At both locations, the DSWC occupied the bottom 20–30 m of the water column and extended to water depths 80 m and 150 m at Two Rocks and Pilbara, respectively. Here, the denser water along the seabed contained cooler, more saline water originating from the shallower inner shelf region. In the relatively narrow and shallow shelves considered here and in the absence of any major river inputs there were no multiple water masses with similar density.

The SST climatology for May/June indicated a narrow band of colder water adjacent to the coast due to heat loss in the shallow waters (Fig. 2). Ocean glider data, collected during the same period, indicated the continuation of this cooler water along the seabed extending further offshore. Higher salinity water is derived from evaporation during summer/autumn (Figure S1). Thus, during this period both temperature (cooling) and salinity (evaporation) contributed to the formation of the DSWC.

Evidence of DSWCs were found in all ocean glider deployments conducted north of 36°S around the Australian coastline, particularly during the winter months. At all of these locations, temperature was the main driver (as seen by the cooler water at the coast, Fig. 2). The locations consisted of a range of tidal and wind forcing: tidal ranges ranged from 0.6 m at Two Rocks to 10 m in the Kimberley whilst the maximum wind speeds ranged from 5.5 ms−1 to > 15 ms−1 at Two Rocks and Investigator Strait (Table 1). Also at all these locations, freshwater discharge was minimal during the austral late autumn and winter months. The DSWCs extend to a distance > 50 km (Kimberley, Fig. 3i) and to depths > 150 m (Pilbara and Yamba, Figures 3ii,vi). The height of the DSWC was a maximum (>50 m) in the Kimberley whilst at all of the other locations the thickness varied between 20–30 m (Fig. 3).

### Seasonal variability

Majority of the ocean glider data were collected from Kimberley, Pilbara, Two Rocks, Investigator Strait and the Great Barrier Reef (Fig. 5) and seasonal cross-shelf density transects from the first 3 locations are presented in Fig. 4. Seasonal variability in these three locations was due mainly to changes in the wind field and air-sea fluxes. The winds are stronger during the summer months due to synoptic winds and strong sea breezes. Similarly, there was strong solar heating/evaporation during the summer months and cooling of the shallower water during late autumn/winter months (Fig. 2 and S1, see Supplementary). This variability was reflected in the seasonal cross-shelf transects. During the summer months, stronger winds mixed the upper ocean resulting in deep mixed layers (>50 m) in the Kimberley and Pilbara (Fig. 5a,e) and upwelling at Two Rocks (Fig. 5i) due to southerly (upwelling favourable) winds. Kimberley and Pilbara transects also show evidence of internal waves (Fig. 5a,e). This region has been documented to experience large internal waves that are generated by the semi-diurnal tide34. In autumn, Kimberley and Pilbara transects were very similar to that for summer, although there was no internal wave activity at Pilbara (Fig. 5f). At Two Rocks, DSWC was initiated (Fig. 5j) mainly due to reduction in wind speeds allowing for higher salinity water to exit the shelf5. During winter, DSWC was present along all three locations driven by surface cooling (Fig. 5c,g,k). In the Kimberley, tidal mixing allowed for vertical mixing of the water column in shallower waters and with increasing depth the diminishing influence of the tidal mixing allowed for the presence of DSWC (Fig. 5c). At all three locations denser water was present closest to the coast with vertically stratified water on the continental shelf. The cross-shelf density gradients at Kimberley, Pilbara and Two Rocks were: −0.512 × 10−5 kgm−4 (Fig. 5c), −1.423 × 10−5 kgm−4 (Fig. 5g), −1.768 × 10−5 kgm−4 (Fig. 5j), respectively. During spring there was no DSWC present at any of the locations with upwelling dominating (at Kimberley and Pilbara due to south-westerly winds and at Two Rocks due to southerly winds).

The main driving force for DSWC formation was the cross-shelf density gradient ($$\frac{\partial \rho }{\partial x}$$; see Eqs. 2 and 6) and the ocean glider data were used to calculate the seasonal variability in $$\frac{\partial \rho }{\partial x}$$ (Fig. 6). In general, at all five locations, $$\frac{\partial \rho }{\partial x}$$ was negative during the cooler months showing the dominance of winter cooling in controlling $$\,\frac{\partial \rho }{\partial x}$$. During the austral summer months (January, February, no data were collected during December), $$\frac{\partial \rho }{\partial x}$$ was positive at all 5 locations and transited to negative values in March and remained negative to August, although at Two Rocks and Investigator Strait the negative $$\frac{\partial \rho }{\partial x}$$ persisted until November (Fig. 6). The timing of the minimum $$\frac{\partial \rho }{\partial x}$$ (i.e. maximum forcing) occurred in July at Kimberley and Pilbara, June in Investigator Strait and in May at Two Rocks. The maxima in May for Two Rocks reflect the combined influence of both salinity and temperature contributing to $$\frac{\partial \rho }{\partial x}$$5. The $$\frac{\partial \rho }{\partial x}$$was largest at Two Rocks when compared to other locations reaching a maximum of −3.0 × 10−5 kgm−4 whist at Investigator Strait, Pilbara and Kimberley the maximum values were: −1.878 × 10−5 kgm−4, −0.829 × 10−5 kgm−4 and −0.487 × 10−5 kgm−4, respectively (Table 1). The $$\frac{\partial \rho }{\partial x}$$along the east coast ranged between −0.982 × 10−5 kgm−4 (Capricorn Channel) and −0.366 × 10−5 kgm−4 (Port Stephens) (Table 1).

### Balance between stratification and mixing

Formation of DSWC is dependent on the ability of the buoyancy input (the stratifying force) through the cross-shelf density gradient $$(\frac{\partial \rho }{\partial x})$$ to overcome vertical mixing (destratifying force) provided by input of turbulent kinetic energy through wind and tidal action (Eqs. 2 and 6). Data from the 254 transects obtained under varying wind and tidal conditions were examined for the presence of DSWC and were related to local wind and tide conditions. The values of the individual terms in Eq. 6 are presented in Fig. 7. The observation sites in this study consisted of a gradual varying (small slope) continental shelves with mean depths of 40–50 m with exception of Investigator Strait which had a mean depth of 70 m. The cross-shelf density gradient, $$\frac{\partial \rho }{\partial x}$$was negative for majority (75%) of transects examined with ~ 50% of $$\frac{\partial \rho }{\partial x}$$ in the range 0 to −1.5 × 10–5 kgm−4 (Fig. 7a). Main variables in Eq. 6, $$\frac{\partial \rho }{\partial x}$$, W3 (proxy for wind mixing) and U3 (proxy for tidal mixing) were also evaluated to examine the relative magnitude of the terms and the presence of DSWC. The results indicated that the main parameter controlling the DSWC was $$\frac{\partial \rho }{\partial x}$$: when $$\frac{\partial \rho }{\partial x}$$ < 0, DSWC was present; whilst $$\frac{\partial \rho }{\partial x}$$ > 0 inhibited the presence of DSWC (Fig. 7b,c). The largest variation in tidal mixing energy was at Kimberley with a maximum tidal range of 10 m. Here, although $$\frac{\partial \rho }{\partial x}$$ was relatively small (>−1.0 × 10–5 kgm−4; Fig. 7c), DSWCs were present even when the maximum currents were up to 0.50 ms−1 (U3 = 0.15 m3s−3). At other locations, tidal mixing was negligible (Fig. 7c). Wind mixing included a range wind speeds (maxima > 15 ms−1) and, except for 5 points at Two Rocks, there was DSWC present whenever $$\frac{\partial \rho }{\partial x}$$ < 0. The 5 points where $$\frac{\partial \rho }{\partial x}$$ < 0 that did not indicate the presence of DSWC corresponded to winds associated with the passage of storm fronts that promoted downwelling30.

### DSWC as a conduit for chlorophyll, backscatter and dissolved oxygen

The Slocum ocean gliders contained a WETLabs BBFL2SLO 3 parameter optical sensor that measured chlorophyll fluorescence (a proxy for phytoplankton biomass), coloured dissolved organic matter (CDOM), and volume backscatter at 660 nm (a proxy for suspended material) and an Aanderaa dissolved oxygen (DO) Optode that collected data simultaneously with the temperature and salinity profiles35,36. Examples of these data streams from Two Rocks and Pilbara (Fig. 8) indicated that bottom layer associated with DSWC consisted of elevated fluorescence and backscatter values (Fig. 8b,c,f,g). The study region is strongly oligotrophic as there are no major terrestrial sources or upwelling for the supply of nutrients and therefore, water column nutrient concentrations are very low. There are no major river inputs resulting in very clear waters with photosynthesis occurring in depths up to 150 m36. In contrast to other regions there is no spring phytoplankton bloom; the seasonal chlorophyll concentrations show maxima during winter due to remobilisation of nutrients from sediments37. Fluorescence distribution in Pilbara indicated higher values in the bottom to water depths 70 m when there was an abrupt shift with higher values at the surface (Fig. 8f). This change was associated with a strong local horizontal density gradient in the bottom layer and elevated backscatter at the shelf edge (Fig. 8f), most likely due to breaking internal waves38. In terms of suspended material, at Two Rocks the backscatter signal extended to water depth of 150 m (Fig. 8c) subsequent to resuspension due to storm activity36. At Pilbara, DSWC contained elevated backscatter values across the shelf (Fig. 8g). A maxima in the backscatter was located at the shelf break due to resuspension by internal waves38. The DSWC was also associated with lower dissolved oxygen values (saturation levels ~ 75%) in the bottom layer. This was due to higher productivity of nutrient supply from the sediments36,37 and strong vertical stratification, due to the presence of DSWC inhibiting vertical mixing (Fig. 8d,h). At both locations the DSWC acted as a conduit to transfer chlorophyll and suspended matter across the continental shelf into deeper water (Fig. 8).

## Discussion

Terrestrial inputs from both natural and anthropogenic influences are discharged into the coastal margin and are transported along-shore and cross-shore by prevailing hydrodynamic conditions that are controlled by the local tidal, wind and buoyancy forcing1,2. In general, along-shore transport, with the land mass providing a barrier, is much stronger than the cross-shore, however, the weaker cross-shore transport is critical for the offshore transport of material from the coastal zone2.

Majority of coastal regions globally are dominated by freshwater inputs from rivers but regions, particularly those experiencing Mediterranean climates experience high evaporation during the summer months and cooling during the winter. Many of these regions are characterised by inverse estuaries and embayments where evaporation exceed freshwater input and the upper reaches contain denser water when compared to those at the seaward margin. As a result, differences in density, estuaries are characterized by longitudinal density gradients that may drive residual circulation with denser water flowing beneath less dense water under the influence of gravity9. In continental shelf regions similar processes operate and recent studies have documented this process, termed Dense Shelf Water Cascade (DSWC) from both field measurements5,13,30,39,40,41 and numerical model simulations29,42,43. These studies were limited to specific locations and did not examine the seasonal variability and its forcing mechanisms. In shallow continental shelf regions, the dynamical balance consists of buoyancy, Coriolis, and friction terms, and hence DSWC moves offshore at an angle to the coastline23. This paper used an extensive multi-year ocean glider data set obtained from 8 locations around the Australian continent under a range of incident tide and wind conditions that also enabled us to resolve seasonal variability.

In coastal and estuarine systems, vertical mixing by wind and tide acts to break down stratification and ultimately determines the vertical structure of the water column and thus the strength of the gravitational circulation24,44. Horizontal Richardson number (Rix), also defined as the Simpson number (Eq. 1), is a measure of the balance between longitudinal density gradient (stratifying force) to vertical mixing (destratifying force)24,26,27. Evaluating Eq. 2 using data obtained from this study indicated that Rix was O(1) indicating dominance of stratification by horizontal density gradients over tidal and wind mixing leading to a stratified water column26.

Data presented in this study indicated that the presence of DSWC was controlled by the cross-shelf density gradient, $$\frac{\partial \rho }{\partial x}$$except under very strong wind speeds: when $$\frac{\partial \rho }{\partial x}$$ < 0, DSWC was present; whilst when $$\frac{\partial \rho }{\partial x}$$ > 0 there was no DSWC (Fig. 7b,c). The maximum $$\frac{\partial \rho }{\partial x}$$ recorded during this study was −3 × 10–5 kgm−4 (Fig. 6). A similar value was reported by Shearman and Brink13 for the north-west of Australia. In comparison, freshwater dominated systems such as the York River estuary24 (USA), $$\frac{\partial \rho }{\partial x}$$is a factor 10 larger at −30 × 10–5 kgm−4 and Liverpool Bay45 (UK) was −10 × 10–5 kgm−4. Coastal embayments that have inverse estuarine behaviour: Shark Bay, Spencer Gulf and the upper Gulf of California have values of −20, −5 and −6 × 10–5 kgm−4, respectively. In the mid-Atlantic Bight $$\frac{\partial \rho }{\partial x}\,$$ = −2 × 10–5 kgm−4 and was associated with winter cooling43. Thus although $$\frac{\partial \rho }{\partial x}$$ was the dominant factor that controlled the presence of DSWC the values recorded by the ocean glider data were comparable to those reported in open coastlines elsewhere. This leaves the possibility that as higher resolution data become available it is possible that many more regions with DSWC may be discovered.

Previous studies have shown that DSWC are persistent features that exist over extended periods at seasonal time scales. The cascades may be interrupted by local wind and tidal conditions that occur over periods of a few days but they reform after such events30. During these events, vertical mixing energy provided by tidal and/or wind action overcomes the buoyancy input through the cross-shelf density gradient. After the cessation of the event, buoyancy input dominates and DSWC is re-established21. The tidal and wind induced mixing terms (Eq. 6), represent scalar quantities and therefore do not include wind direction and/or changes in tidal range (e.g. spring-neap cycle). We now consider the influence of tidal range and wind direction on DSWC. Vertical mixing of the water column occurs through turbulent kinetic energy (TKE) generated by the action of tides and winds. Tidal action generates TKE at the seabed that is advected upwards from the seabed into the water column. In contrast, wind generates TKE at the air-sea interface that is advected downwards from the sea surface6. The main temporal variability in tidal mixing is due to the fortnightly spring-neap cycle with increased mixing energy during spring tides. If the tidal mixing energy is able to mix the whole water column then DSWC does not exist. However, at all of the locations examined here, particularly in the Kimberley region where the tidal range is 10 m and maximum bottom currents > 0.50 ms-1, DSWC were present irrespective of the tidal stage (i.e. within a tidal cycle or over the spring-neap cycle) indicating that buoyancy input was the dominant factor. The influence of the spring-neap cycle was to change the extent of DSWC above the seabed (smaller height during neap tides) indicating that the tidal mixing did not extend through the whole water column.

The influence of wind speed and direction also has an influence and can be summarised as follows1,6,20,21,46. in the presence of a negative cross-shelf density gradient (denser water near shore, lighter far from the coast), onshore (offshore) winds enhanced (decreased) the vertical stratification and decreased (increased) the cross-shelf density gradient. Mahjabin et al.30 characterised the influence of wind speed and direction on the occurrence of DSWC and concluded that in the presence of a negative cross-shelf density gradient (-d𝜌/dx), DSWC’s were always present under low wind conditions. When there was an onshore component of wind (downwelling favourable) the DSWC was enhanced through strengthening of the (-d𝜌/dx). With an offshore component of wind there was vertical mixing as denser water was advected over lower less dense water (‘straining’). The mixing events that interrupted the DSWC lasted only for a few days and after the cessation of the event the DSWC reformed.

Results of this study highlight a unique global feature that occurs in Australian continental shelves where continental scale forcing, at both spatial and temporal scales, dominate the meso-scale and/or local forcing. Typical spatial scales of wind forcing are < 500 km limited by the size of the atmospheric systems and the temporal scale is 5–10 days due to the passage of weather systems. There are large gradients in tidal forcing over spatial scales of ~ 1000 km. In Western Australia, over a 2000 km coastline tidal regime changes from semi-diurnal tides with a 10 m tidal range in the north to diurnal tides with 0.6 m tidal range in the south5. The temporal scale of the tides includes the fortnightly spring-neap cycle. Freshwater inputs are mainly point sources and their influence on the coastal system (ROFI) is generally limited to 100’s of km (<1000 km for the Mississippi). Across the Australian continent, the influence of evaporation and cooling cover a spatial distance > 10,000 km (Figs. 2 and S1, see Supplementary) and a time period of order months. Forcing through air-sea fluxes results in higher density water on the inner shelf particularly during the winter months providing the driving force for the formation of DSWC around the Australian coast. Here, the continental scale forcing through air-sea fluxes overcomes the local wind and tidal forcing.

Cross-shelf transport, to which DSWC is a strong contributor, has a major role in ecosystem functioning and bio-geochemical processes as a conduit for the transport of nearshore water and dissolved and suspended material off the continental shelves2. Instances of strong DSWC events transporting material over distances from the source region have been documented elsewhere47. In the Two Rocks region (Fig. 3) field measurements indicated that, within the DSWC, the mean cross-shelf currents (~ 0.10 ms-1) were comparable to the alongshore currents30. Often it is considered that along-shore currents are much stronger than the cross-shore currents1,2 and thus the higher cross-shore currents within the DSWC is unique. Higher concentrations of chlorophyll and suspended material together with offshore directed currents demonstrate that DSWC may have a major influence on the cross-shelf transport along coastlines extending over 10,000 km. This leads to the conclusion that during the winter months when the coastal regions in Australia are cooling due to heat loss, the inner shelf water exits along the seabed to deeper water, ‘draining’ the system.

## Conclusions

Dense shelf water is formed when the density of the inner shelf water is increased either by a decrease in temperature through cooling and/or an increase in salinity from evaporation. This cross-shelf density gradient drives a gravitational circulation with offshore transport of higher density water along the sea bed. This process is similar to that observed in ‘inverse’ estuarine systems and defined as Dense Shelf Water Cascades (DSWC). Analysis of an extensive multi-year data set obtained using ocean gliders confirmed that, under a range of wind and tidal conditions, DSWCs occurred regularly during autumn and winter months all around Australia’s continental shelves. It is concluded that the cross-shelf density gradient established across the continental shelf through air-sea fluxes (cooling and evaporation) is the primary forcing mechanism for the formation of the DSWC. Data indicated that even in the presence of relatively high wind- and tidally-induced vertical mixing, DSWCs were present due to the strength of the cross-shelf density gradient. Formation of DSWC around Australia is a unique occurrence globally where continental scale forcing through air-sea fluxes overcome the local wind and tidal forcing. The DSWC acts as a conduit for the transport of chlorophyll and suspended material across the continental shelf and is a critical process influencing cross-shelf transport that controls water quality on the inner continental shelf.

## Methods

Water column data were obtained from cross-shelf transects undertaken using Teledyne Webb Research Slocum electric gliders (http://www.webbresearch.com/) from 8 locations around Australia (Fig. 3). The ocean gliders are operated by Integrated Marine Observing System (IMOS) Ocean Glider facility hosted by The University of Western Australia35. All the ocean glider data are publicly available through the Australian Ocean Data Network (https://portal.aodn.org.au). Ocean gliders obtained data from the surface to 2 m above the seabed, travelling at a mean horizontal speed of 25 km per day48. The glider traverses a saw-tooth pattern using buoyancy control whilst moving forward to the target destination and navigates its way to a series of pre-programmed waypoints using GPS, internal dead reckoning and altimeter measurements. The gliders were equipped with a Sea-Bird Scientific SBE 41CP pumped CTD (conductivity–temperature–depth) sensor, a WETLabs BBFL2SLO 3 parameter optical sensor (which measured chlorophyll fluorescence, coloured dissolved organic matter, and backscatter at 660 nm), and an Aanderaa oxygen optode. All the sensors sampled at 4 Hz which yielded measurements 7 cm in the vertical. A single glider mission operated over a period of 25–30 days and traversed ~ 500–600 km and performed ~ 4000 vertical dives. During a single mission many repeat transects across the shelf were completed and depending on the width of the shelf each transect was completed over a period of 2–7 days. In water depths of 40–50 m, the glider takes ~ 20 mins to perform a single dive (i.e. from surface to bottom and return to surface) providing a vertical profile every 10 mins. The horizontal separation of the profiles was ~ 100 m and over a daily cycle ~ 140 vertical profiles were completed.

The focus of this paper is on the temperature and salinity (and density) data. Subsequent to the ocean glider recovery, all the data collected by the glider were subject to QA/QC procedures that include a series of automated and manual tests49. IMOS data streams are provided in NetCDF-4 format with data files containing meta-data and scientific data for each glider mission.

Ocean glider data collected between 2008 and 2019 from 8 different locations (Fig. 3) around the Australian continent were analysed and included 254 transects selected from 126 ocean glider deployments each lasting 20–25 days. This is equivalent to > 2700 days of continuous ocean profiles. The data set included a total of 275547 vertical profiles and over 84 million data scans in total. The analyses presented here is limited to the top 150 m of the water although the glider acquired data to a maximum depth of 200 m.

The horizontal density gradients were calculated by subtracting the depth-mean density at a point closest to the coast from the depth-mean density at a point at the seaward end of the transect and dividing by the distance between the two points. The resulting density gradient was defined to be negative when the nearshore water was denser than offshore.

The 8 locations around Australia (Fig. 3) were selected based on the availability of ocean glider data35. These locations have contrasting tidal (0.6 to 10 m tidal range) and wind (maximum wind speeds > 15 ms-1) forcing and include: (1) The Kimberley, north-west Australia: macro-tidal and moderate winds13; (2) The Pilbara, north-west Australia: macro-tidal50; (3) Two Rocks, Western Australia: wind dominated21,41 with low tidal range and diurnal tides51; (4) Investigator Strait, South Australia: tidally dominated52,53; (5) Port Stephens, New South Wales: macro tides54 and strong winds55; (6) Yamba, New South Wales: mostly wind driven and micro-tidal56; (7) Capricorn Channel, Queensland: moderate winds and macro tides57; and, (8) Cooktown, Queensland: moderate winds and macro tides58,59. A summary of the study locations and associated maximum cross-shore density gradients estimated from ocean glider data are shown in Table 1.

Tidal conditions were predicted using the TPXO7.2 global database (http://volkov.oce.orst.edu/tides/TPXO7.2.html) and wind data were obtained from the European Centre for Medium-Range Weather Forecast Interim Reanalysis (ECMWF ERA-I)46 (https://apps.ecmwf.int/datasets/data/interim-full-daily/levtype=sfc/). Terms in Eq. (3) were evaluated through estimates of local wind speed cubed (|W3 | ) and bottom current speed cubed (|U3 | ).

Although data from 8 locations were available; only 5 locations Kimberley, Pilbara, Two Rocks, Investigator Strait and Cooktown (Fig. 3) contained data throughout the whole year to define the seasonal variability. The mean horizontal density gradient for each month of the year was calculated using multiple transects acquired over several years. Two Rocks contained the highest repeating missions of ~ 44, and other locations: Kimberley, Pilbara, Investigator Strait and Cooktown consisted of 15, 12, 16 and 71 missions respectively. Error bars show minimum and maximum density gradients for each month at each of the 5 locations spread over different years (Fig. 6).

## Data availability

All the data used in this paper are available from the data portal of the Integrated Marine Observing System (IMOS): https://portal.aodn.org.au/. Tidal data are predicted from TPXO7.2 global database and wind data are obtained from the European Centre for Medium-Range Weather Forecast Interim Reanalysis (ECMWF ERA-I).

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## Acknowledgements

All ocean glider data used in this paper were sourced from Australia’s Integrated Marine Observing System (IMOS) data portal (https://portal.aodn.org.au/). IMOS is enabled by the National Collaborative Research Infrastructure Strategy (NCRIS). It is operated by a consortium of institutions as an unincorporated joint venture, with the University of Tasmania as Lead Agent. The ocean glider data were collected by the IMOS Ocean Glider facility located at the University of Western Australia. The authors acknowledge the support of Dennis Stanley, Paul Thomson, Kah Kiat Hong and Mun Woo for the tasks associated with the deployment and recovery of the gliders, glider piloting and processing the data QA/QC of the ocean gliders. This postgraduate research has been funded by Scholarship International Research Fees (SIRF), University International Stipend, University Postgraduate Award and Ad Hoc Postgraduate Scholarship.

## Author information

Authors

### Contributions

This study was done as a part of PhD research by T.M. All ocean glider data analysis were done by T.M. with supervision of C.P. and Y.H. All authors contributed to preparation of the manuscript.

### Corresponding author

Correspondence to Tanziha Mahjabin.

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### Competing interests

The authors declare no competing interests.

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Mahjabin, T., Pattiaratchi, C. & Hetzel, Y. Occurrence and seasonal variability of Dense Shelf Water Cascades along Australian continental shelves. Sci Rep 10, 9732 (2020). https://doi.org/10.1038/s41598-020-66711-5